You are choosing between two projects. The cash flows for the projects are given in the following table ($ million): Project Year 0 Year 1 Year 2 Year 3 Year 4 A negative $ 48−$48 $ 27$27 $ 21$21 $ 21$21 $ 13$13 B negative $ 98−$98 $ 22$22 $ 39$39 $ 48$48 $ 60$60 a. What are the IRRs of the two projects? b. If your discount rate is 4.6 %4.6%, what are the NPVs of the two projects? c. Why do IRR and NPV rank the two projects differently?
PROJECT A
0 = -$48 + $27/(1+ IRR)1 + $ 21/ (1+IRR)2 + $21/(A+IRR)3 + $13/(1+IRR)4
IRR = 29%
IRR = Where NPV is equal to Zero
Using trial and error approach we get
Year | Cash flow | PVF(29%) | PVCF(29%) | PVF(30%) | PVCF(30%) |
0 | -48 | 1 | -48 | 1 | -48 |
1 | 27 | 0.775194 | 20.93 | 0.769231 | 20.77 |
2 | 21 | 0.600925 | 12.62 | 0.591716 | 12.43 |
3 | 21 | 0.465834 | 9.78 | 0.455166 | 9.56 |
4 | 13 | 0.361111 | 4.69 | 0.350128 | 4.55 |
NPV | 0.03 | -0.69 |
IRR = 29% + (0.03-0)/(0.03 - (-.69))
= 29.04%
PROJECT B =
0 = -$98 + $22/(1+ IRR)1 + $ 39/ (1+IRR)2 + $48/(A+IRR)3 + $60/(1+IRR)4
IRR = 21.89%
IRR = Where NPV is equal to Zero
Using trial and error approach we get
Year | Cash flow | PVF(21%) | PVCF(21%) | PVF(22%) | PVCF(22%) |
0 | -98 | 1 | -98 | 1 | -98 |
1 | 22 | 0.826446 | 18.18 | 0.819672 | 18.03 |
2 | 39 | 0.683013 | 26.64 | 0.671862 | 26.20 |
3 | 48 | 0.564474 | 27.09 | 0.550707 | 26.43 |
4 | 60 | 0.466507 | 27.99 | 0.451399 | 27.08 |
NPV | 1.90 | -0.25 |
IRR = 21% + (1.9-0)/ (1.9 - (-.25))
= 21.89 %
b)
NPV
Project A
Year | Cash flow | PVF(4.6%) | PVCF(4.6%) |
0 | -48 | 1 | -48 |
1 | 27 | 0.956023 | 25.81 |
2 | 21 | 0.91398 | 19.19 |
3 | 21 | 0.873786 | 18.35 |
4 | 13 | 0.835359 | 10.86 |
NPV | 26.22 |
Project B
Year | Cash flow | PVF(4.6%) | PVCF(4.6%) |
0 | -98 | 1 | -98 |
1 | 22 | 0.956023 | 21.03 |
2 | 39 | 0.91398 | 35.65 |
3 | 48 | 0.873786 | 41.94 |
4 | 60 | 0.835359 | 50.12 |
NPV | 50.74 |
c)
NPV and IRR rank the two projects differently because they are measuring different things. NPV is measuring value creation, while IRR is measuring return on investment. Because returns do not scale with different levels of investment, the two measures may have different rankings when the initial investments are different.
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